An equivalent form of Young's inequality with upper bound

Young's integral inequality is complemented with an upper bound to the remainder. The new inequality turns out to be equivalent to Young's inequality, and the cases in which the equality holds become particularly transparent in the new formulation.Comment: 5 pages. v2: Title changed to match published version. Previous title: "Doubling Young's inequality

Differential aging from acceleration, an explicit formula

We consider a clock 'paradox' framework where an observer leaves an inertial frame, is accelerated and after an arbitrary trip comes back. We discuss a simple equation that gives, in the 1+1 dimensional case, an explicit relation between the time elapsed on the inertial frame and the acceleration measured by the accelerating observer during the trip. A non-closed trip with respect to an inertial frame appears closed with respect to another suitable inertial frame. Using this observation we define the differential aging as a function of proper time and show that it is non-decreasing. The reconstruction problem of special relativity is also discussed showing that its, at least numerical, solution would allow the construction of an 'inertial clock'.Comment: Revtex4, 5 pages, 1 fugur

A unifying mechanical equation with applications to non-holonomic constraints and dissipative phenomena

A mechanical covariant equation is introduced which retains all the effectingness of the Lagrange equation while being able to describe in a unified way other phenomena including friction, non-holonomic constraints and energy radiation (Lorentz-Abraham-Dirac force equation). A quantization rule adapted to the dissipative degrees of freedom is proposed which does not pass through the variational formulation.Comment: Latex2e, 10 pages. V2: some corrections in Sect.